SOLUTION: A homing device left its home to deliver a message. On takeoff the device encountered a tailwind of 9 mph and made the delivery in 20 minutes. The return trip into the wind took 40

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Question 778647: A homing device left its home to deliver a message. On takeoff the device encountered a tailwind of 9 mph and made the delivery in 20 minutes. The return trip into the wind took 40 minutes. How fast could the device fly in still air?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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A homing device left its home to deliver a message.
On takeoff the device encountered a tailwind of 9 mph and made the delivery in 20 minutes.
The return trip into the wind took 40 minutes.
How fast could the device fly in still air?
:
Let s = speed in still air
then
(s+9) = relative speed with the wind
and
(s-9) = relative speed against
:
Change 20 min to 1/3 hr. Change 40 min to 2/3 hr
:
Write a distance equation, distance there and back are the same
2%2F3(s-9) = 1%2F3(s+9)
multiply both sides by 3, resulting in:
2(s-9) = s + 9
2s - 18 = s + 9
2s -s = 9 + 18
s = 27 mph speed in still air
:
:
Confirm this by finding the actual distances
2%2F3*(27-9) = 12 mi
1%2F3*(27+9) = 12 mi